A 85-kg astronaut pushes to the left on a spacecraft with a force F in “gravity-free” space. The spacecraft has a total mass of 1.0 × 10^4 kg. During the push, the astronaut accelerates to the right with an acceleration of 0.36 m/s^2.
Which one of the following statements concerning this situation is true?
A) The spacecraft does not move, but the astronaut moves to the right with a constant speed.
B) The astronaut stops moving after he stops pushing on the spacecraft.
C) The force exerted on the astronaut is larger than the force exerted on the spacecraft.
D) The force exerted on the spacecraft is larger than the force exerted on the astronaut.
E) The velocity of the astronaut increases while he is pushing on the spacecraft.
Determine the magnitude of the acceleration of the spacecraft.
A) 30.6 m/s2
B) 0.36 m/s2
C) 2.5 × 10–3 m/s2
D) 7.0 × 10–3 m/s2
E) 3.06 × 10–3 m/s2
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The correct statement is E) The velocity of the astronaut increases while he is pushing on the spacecraft. This is because the astronaut is exerting a force on the spacecraft, which according to Newton's third law, means the spacecraft is exerting an equal and opposite force on the astronaut. This force causes the astronaut to accelerate to the right.
To determine the magnitude of the acceleration of the spacecraft, we can use Newton's second law, F = ma. The force exerted on the spacecraft is equal to the force exerted by the astronaut, which can be found by multiplying the astronaut's mass by his acceleration (F = ma = 85 kg * 0.36 m/s^2 = 30.6 N). The acceleration of the spacecraft is then found by dividing this force by the mass of the spacecraft (a = F/m = 30.6 N / 1.0 × 10^4 kg = 3.06 × 10–3 m/s^2). So, the correct answer is E) 3.06 × 10–3 m/s^2.
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